Normally a transformer has separate primary and secondary windings. But the auto transformer is a special transformer which has a common winding both for the primary and secondary windings.
The auto transformer consists of only one winding wound to a laminated magnetic core with a rotary moveable contact point. These transformers can be used as a step up or a step down transformer.
The auto transformer provides a higher efficiency at a low cost as compared to a two winding transformer. It is also smaller in size.
Auto transformer are used in dimmer stat, variac(To vary the supplied voltage), to start an AC machine, etc…